Data Interpretation curriculum

Before reading a value, check what one unit on the axis stands for and in what units. A bar at 7.5 on an axis labeled "thousands of visitors" means 7,500 visitors, and a column headed $k is in thousands of dollars. A misread scale makes every answer wrong by the same factor, and the trap choices are usually built from that factor.

Questions such as "which day sold the most?" want a label, not a number. If Monday to Thursday sold 31, 46, 28, and 39, the answer is Tuesday; 46 is the evidence. Read the question's last words to see whether it asks for a day, a month, a category, or an amount.

To find the largest value, make one pass through the data and keep only the current leader in mind, replacing it whenever a bigger value appears. Rereading the whole table for each comparison is slower, and it is where a larger value gets missed. The same pass finds the smallest value.

With grouped bars or several lines, identify which color, pattern, or line style belongs to which series before comparing anything. Swapping two series gives answers that look reasonable and are wrong. Check the legend again whenever the question names a series, such as "Product B" or "City A".

Add a list by pairing values whose ones digits make 10 before adding the rest: for sales of 26, 18, 34, and 22, pair 26 + 34 = 60 and 18 + 22 = 40, for 100 in all. Pairing removes most of the carrying, which is where list totals usually go wrong. Count the values first so none is skipped.

When the total and all but one part are known, add the known parts and subtract. A yearly total of 604 with the first three quarters at 140, 95, and 158 leaves 604 − 393 = 211 for the fourth quarter. Adding the total to the parts, or forgetting one part, are the usual slips.

To find when a cumulative total first passes a target, keep a running sum and stop at the first value above it. Daily sales of 18, 27, 9, and 33 give running totals of 18, 45, 54, and 87, so a target of 80 is first passed on the fourth day. Comparing single days to the target instead answers a different question.

To compare the best value with the second-best, find both before subtracting: in 44, 61, 38, and 57, the best is 61 and the second-best 57, so the gap is 4. Subtracting the smallest value instead gives the range, 23, which is a different question and a common trap.

The difference between the wettest and driest months is the largest value minus the smallest. For monthly rainfall of 62, 18, 47, and 71 mm, that is 71 − 18 = 53 mm. Name both extremes before subtracting, since a difference between two neighboring months is a different question.

To find where a series fell the most, compute each step's change with its sign. For 66, 41, 52, 19, the changes are −25, +11, and −33, so the biggest fall is from the third value to the fourth. A large rise is not a fall, and comparing the sizes without signs picks the wrong pair.

Subtract by counting up from the smaller number through a round number: from 27 up to 30 is 3, and from 30 up to 84 is 54, so 84 − 27 = 57. Counting up avoids borrowing, which is where most subtraction slips happen.

An absolute change is a difference in amounts; a relative change compares that difference to the starting amount. A rise of 15 is half of a starting value of 30 but only a twentieth of 300. Read whether the question asks "how many more" or "by what percent" before computing.

The mean is the sum divided by the count: temperatures of 18°, 23°, 15°, and 20° total 76, so the mean is 76 ÷ 4 = 19°. A mean must lie between the smallest and largest values, so an answer outside that range signals an arithmetic slip.

When one value joins a group, the new average is the old total plus the new value, divided by the new count. A crew of 6 averaging 12 km, joined by a member who logs 26 km, averages (72 + 26) ÷ 7 = 14 km. Averaging the old average with the new value treats the newcomer as half the group.

To combine groups of different sizes, combine their totals. A branch of 20 staff averaging $60k and another of 60 averaging $80k total $1,200k and $4,800k, so the combined average is $6,000k ÷ 80 = $75k, not the $70k midpoint. The larger group pulls the result toward its own average.

A slice of a pie chart is its percent of the whole: a 35% slice of a $1,400 budget is 0.35 × 1,400 = $490. Convert the percent to a decimal and multiply by the total the chart describes, not by another slice.

If one slice's amount and percent are known, divide to find the whole. If cookies are 15% of sales and sold 90 units, total sales were 90 ÷ 0.15 = 600 units. Multiplying 90 by 15% instead finds a percent of the slice, a much smaller and meaningless number.

Slices of a pie chart add to 100%, so a slice described as "the rest" is 100% minus the labeled ones. With slices of 38% and 47%, the rest is 15%. Use that percent with the total, or with the slice's amount, as the question requires.

A percent change divides the change by the starting value. From 76 to 95 is a rise of 19 on 76, a 25% increase. From 95 down to 76 is a fall of 19 on 95, a 20% decrease. The same change gives different percents in the two directions, because the starting values differ.

A share of a share multiplies the rates. If 45% of 800 people own a car and 30% of those also own a bike, then 0.45 × 0.3 = 0.135 of all 800 own both, which is 108. Applying the 30% to the whole 800 ignores the words "of those".

For "what percent of the cyclists are women", divide by the cyclists. In a survey of 50 women, 15 of whom cycle, and 100 men, 45 of whom cycle, there are 60 cyclists, and 15 of them, or 25%, are women. Dividing 15 by the 50 women gives 30%, which answers a different question.

Growth over several periods multiplies. Growth of 10% and then 40% gives 1.1 × 1.4 = 1.54, a total of 54%, not 50%, because the second rate applies to the already larger amount. Convert each rate to a factor, multiply, and convert back.

Compare counts from groups of different sizes as rates. A town of 30,000 with 90 thefts has 3 per 1,000 people, and a town of 75,000 with 150 thefts has 2 per 1,000, so the town with fewer thefts has the higher rate. Raw counts favor the bigger group.

A market share is a company's sales divided by the whole market. If a company's sales stay at 60 while the market grows from 300 to 400, its share falls from 20% to 15%. Unchanged sales can mean a shrinking share whenever the whole grows.

A price index sets its base year to 100, so the index divided by 100 is the price multiplier. An index of 135 means prices are 1.35 times the base year's, so a $240 basket then costs $324 now. Reading the index as a percent increase of 135% is the classic error.

To find what fraction of a total one part represents, divide the part by the sum of all parts: a quarter with 90 of the year's 360 sales holds one quarter of the total. Dividing by another part, or by the largest bar, gives the wrong fraction.

A scatter plot shows a positive relationship when the points rise from left to right, a negative one when they fall, and no clear relationship when they form a shapeless cloud. A relationship in a scatter plot does not by itself show that one variable causes the other.

In a grouped bar chart, a question about combined totals needs the bars in each group added before the groups are compared. The tallest single bar does not mark the highest combined total, because a group of two medium bars can outsum one tall bar and one short bar.

Where two lines on a chart are farthest apart is the point with the largest vertical gap between them, not the highest point of either line. Compare the differences at each point, and note which line is on top, since the gap can change sign when the lines cross.

A claim such as "increased every quarter" holds only if every step rises. One dip disqualifies the series, however high it ends. Check each consecutive pair rather than comparing the first and last values.

Many wrong choices are right answers to a neighboring question: the value instead of the label, a part instead of the total, the change instead of the new amount, or the range instead of the gap between the top two. Reread the last sentence of the question before choosing.

The data sets bounds an answer must respect. A mean lies between the smallest and largest values, a part cannot exceed its total, a pie chart's slices add to 100%, and a combined average lies between the group averages. An answer outside those bounds is wrong.

Round the values and estimate before computing exactly: sales of 26, 18, 34, and 22 are about 30 + 20 + 30 + 20 = 100. A computed total far from the estimate signals a skipped value or a carrying slip, and the estimate alone often rules out most choices.